We make a precise recommendation for the choice of dissection sets for George’s [4] nested dissection on a square $n \times n$ grid with n not a power of 2 and make some experimental comparisons with the direct use of the minimal degree algorithm of Markowitz [5]. Our results additionally indicate that the performance of the minimal degree algorithm can be significantly influenced by the way in which ties are broken. We also discuss the dissection of irregularly shaped regions and the extension of George’s ordering to three-dimensional regions.